Matrix Product Renormalization Group: Potential Universal Quantum Many-Body Solver

TL;DR

The paper introduces the matrix product renormalization group (MPRG), an advanced tensor network algorithm that aims to be a universal and versatile solver for quantum many-body problems across various conditions and systems.

Contribution

It presents MPRG as a novel, non-variational tensor network method capable of handling zero and finite temperatures, higher dimensions, and non-Hermitian systems.

Findings

Successfully computed critical properties of Yang-Lee edge singularity.

Demonstrated applicability to non-Hermitian quantum systems.

Potential to unify various quantum many-body solving techniques.

Abstract

The density matrix renormalization group (DMRG) is a celebrated tensor network algorithm, which computes the ground states of one-dimensional quantum many-body systems very efficiently. Here we propose an improved formulation of continuous tensor network algorithms, which we name a matrix product renormalization group (MPRG). MPRG is a universal quantum many-body solver, which potentially works at both zero and finite temperatures, in two and higher dimensions, and is even applicable to open quantum systems. Furthermore, MPRG does not rely on any variational principles and thus supports any kind of non-Hermitian systems in any dimension. As a demonstration, we present critical properties of the Yang-Lee edge singularity in one dimension as a representative non-Hermitian system.